On the distribution of angles between the N shortest vectors in a random lattice

Details On the distribution of angles between the N shortest vectors in a random lattice On the distribution of angles between the N shortest vectors in a random lattice

2010-12-15

arxiv.org/abs/1012.3376v1

Journal of the London Mathematical Society 84 (2011) 749-764

Mathematics

Number Theory

17 pages

Scientific paper

We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n tends to infinity. Moreover we interpret the result in terms of eigenvalues and eigenfunctions of the Laplacian on flat tori. Finally we discuss the limit distribution of any finite number of successive minima of a random n-dimensional lattice as n tends to infinity.

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